What do you begin an astronomy course with? A first taste of the constellations? Celestial co-ordinates? Physics? History? I have found that the point never fails to come, either in these lessons or in later ones, where I am glad I can say (or wish I could say): "You remember how in the planet-walk we saw that..."
I conclude that this should be the first lesson, the aperitif, or at most the second. Tell the students: "Astronomy is an outdoor subject, and even though it's now daytine" (or, "is cloudy") "we're going right outside for our first exercise!" It will wake them up, make them think you are a lively teacher, leave them with a sense of expecting future lessons to be fun too (so that- don't be alarmed!-they will actually classify the rest of the course as fun even if some of it isn't).
Point out that the nine planets do not stay in a straight line. They stay about the same distances from the Sun, but circle around it (counterclockwise as seen from the north).
They go around at various speeds. The inner planets not only have smaller circles to travel but move faster. Thus, Mercury goes around in about 3 months; the Earth, in a year; and Pluto in about 250 years.
The circling movements mean that the planets spend most of their time much farther apart even than they appear in out straight-line model. The distance between two planets can be up to the sum of their distances from the sun, instead of the difference.
Jupiter and Saturn, for instance, can be as close as 95 paces as in the model, or up to 382 paces apart at times when they are on opposite sides of the orbits.This is the case in the years around 1970,1990, and 2010. (Jupiter overtakes Saturn about every 20th year.) Think of the spacecraft Pioneer 11, which actually covered this immense distance. Launched from Earth in April of 1973, it looped around Jupiter in December 1974, and arched back all the way over the solar system, on its way to visit Saturn also. This journey is so long-the distance back from Jupiter plus the even greater distance out to Saturn-that the spacecraft did not reach Saturn till September 1979. During the Thousand- Yard walk is the dramatic time to tell people about this, and let them reflect on the refinement with which the spacecraft had to be aimed around the south pole of Jupiter in just such a way that it might five years later drop between Saturn (this acorn) and its rings.
Schematic pictures often show the planets on parade at about equal distances- much as when you first arrayed them on the table. This, as we have seen is unrealistic: the intervals are very unequal. There are these features to point out:
So, if you need to fold the walk back on itself, because of not having space to walk a thousand yards, Uranus is the point at which to turn.
Throughout most of human history, only six planets have been known: Mercury, Venus, Earth, Mars, Jupiter, Saturn. (Most of the time nobody knew what planets are or that the Earth is a planet.) Then, in the last three centuries, three new planets were discovered. Uranus, though theoretically visible to the naked eyer on fine nights if you know just where to look, was not noticed till 1718; Neptune was discovered by careful calculation and search in 1846; and Pluto in a similar way, but not till 1930 after a quarter of a century of meticulous search, for even in large telescopes it is lost among countless thousands of equally faint stars.
And anyone who takes our planet-walk will say: "No wonder!"Pluto not only is smaller than the other eight planets, but is smaller than the Moon and half a dozen other satellites of planets. It is, as we have seen, the exception to the rule that the inner planets are small (and rocky) and the outer planets large (and gaseous).
It is also exceptional in its orbit, which somewhat messes up our model.It is true that Pluto's average distance from the Sun is about 3,666,000,000 miles (1,019 paces in our model). But its orbit, instead of being nearly circular like those of the other planets, is very eccentric or elliptical: part of it is much nearer in toward the Sun and part much farther out. At present Pluto is on the inward part. In fact, it is nearer in than Neptune! This is so from 1979 until 1999, when Pluto will again cross outward over Neptune's orbit.
Thus a true statement is that Pluto is usually the outermost known planet (but for just these ten years out of 250 Neptune is) and that the distance in our model from the Sun to the outermost planet is about a thousand yards on average (but it should really vary from only Neptune's 777 yards in these ten years, to as much as 1,275 yards when Pluto is at the outermost part of it orbit).
The other planets circulate in the same plane as the Earth, at least nearly enough that we can represent this by the plane of the ground. But Pluto's orbit is inclined to this general plane by the fairly large angle of 17 degrees. This means that part of the huge orbit lies far above (north of) ours and part far below. At present Pluto is still well to the north side. So if you want to mention this, you can tell the last planet-carrying child to walk 242 paces and then climb a tree-"just kidding..." (Actually the tree should be 200 yards high! And there are parts of the orbit where Pluto should be up an even higher tree or down a very deep hole in the ground.)
When Mars, moving rapidly along its relatively nearby orbit, passes in front of Jupiter or Saturn, and we look at these planets through a telescope, we are surprised to find that the disk of Mars looks much the smaller. Jupiter looks three times as wide as Mars, though it it eight times farther away!
The planet-walk will have impressed you with the great distance from Mars onward to Jupiter, and thus will give this observation its surprising quality. However, the planet-walk also gives you the means to visualize the reason. The farther away two objects are, the less the distance between them counts, and the more it is a matter of their own actual sizes. Or, put another way, angular size decreases slower and slower with distance.
When we first laid the row of objects out on the table, there was an extreme contrast between the Sun and the rest. The word "size" is vague, since it could mean width (diameter), volume, or mass (amount of matter). In volume, the Sun is 600 times greater than all the planets put together. As compared with the small but rather dense Earth, the Sun is 109 times greater in width; 1,300,00 times greater in volume; and 330,000 times greater in mass.
Within the planets themselves, there is quite a contrast between Jupiter and the rest. Jupiter contains almost three times as much matter as all the other planets together-even though Saturn comes a good second to it in width.
This is partly because Saturn is the least dense of all the planets (it would float on water, if there was an ocean big enough). But it is also an illust- ration of the difference between the kins of "size." If you multiply a planet's width by, say, 3, you mutltiply its cross-sectional area by 9, and its volume by 27. Thus a relatively small difference between the widths of Saturn and Jupiter means a much larger difference between their capacity. This, too, is easier to understand when you look at the solid objects representing them.
You can, on reaching the position for the Earth, pause and put down a Moon beside it. This Moon will have to be another pinhead (theoretically between the sizes of Mercury and Pluto).
Look down on this distance, the length of your thumb; the greatest distance that Man has yet leaped from him home planet. Reflect on the manned mission to Mars now being suggested (14 yards in our model) or the trips proposed in science fiction: to Jupiter as in the film 2001 Space Odyssey (109 yards); to the nearest star (four thousand miles in our model); to the Andromeda Galaxy (half a million times farther again).
The planet walk is an antidote to the "scientific" school of astrologers, who suggest that the planets disturb particles in our bodies. When one can visual- ize how remote these planets are, it is easy to understand that the nearest of them, Venus, when nearest to us, has the same gravitational or tidal effect as a truck 14 miles away, or a high-rise building 300 miles away.
During the walk, the immense distances between the planets and the Sun may make people incredulous that the planets can truly feel the gravitational influence of the Sun at all, let alone be so much in its control that they orbit faith- fully around it forever. After all, if our model is to scale, then this peppercorn, representing the Earth, must experience a similar gravitational pull from that far-off ball, representing the Sun. Does it? It certainly shows no inclination to fall toward the ball, and has no need to stave off such a fall by orbitting around the ball!
The peppercorn does feel the gravitational pull of the ball. The difference is that there is so much other matter in the environment of the model, which is not present in the environment of the things being modeled: the sidewalk, the the pillars of the arcade you are walking along, the grass and trees, your feet and above all the air pressing down and the total mass of the Earth underneath. These are all so huge that the atraction of the ball, without becoming any less, becomes by comparison a negligible influence in the distance. If there were, in interplanetary space, any object corresponding to even one of these things - say, a four-million-mile slab of rock, corresponding to the paving-stone on which the peppercorn is lying - then the Sun's influence on the Earth would become negligible. It is only because space is so empty that the Sun is the nearest important gravitational influence on the Earth.
The solar system does not really end with Pluto. Besides the planets, there is a thin haze of dust (some of it bunched into comets). Any of this dust that is nearer to the Sun than to any other star may be in the gravitational hold of the Sun and so counts as part of the solar system. So the outermost of such dust may be half way to the nearest star.
On the scale of our model, Pluto is a thousand yards or rather more than a half a mile out. But this true limit of the solar system is two thousand miles out.
A thousand miles, in our mode, is the distance called a light-year (in reality, about six million million miles).The human mind can never conceive this thing called a light-year, which is the currency of our small-talk about the universe. (It is probable that we cannot directly conceive any distances above about 600 yards, which is where we sub- consciously place the horizon). But through the model we move as far toward conceiving it as we ever can.
I, at least, have seemed to have some respect for the term, light-year; and to have some sense of what I mean when I use it-since I made the sensory approach to it through this model.
The rest of the stars in our galaxy are probably on the order of four to ten light-years apart from each other, as we are from our nearest neighbor.
This is a stunning thought when (having done the Thousand-Yard exercise) you go out at night and look at the Milky Way. It is a haze of light so delicate that it can no longer be seen from inside our light-ridden cities. It consists of the bulk of the stars in our galaxy, piled up in the distance, so numerous and so faint that we cannot see them separately. Yet they are all the same kind of distance from each other as we are from the nearest of them. That is to say, if we could hop to any one of them, cavernous black space would open out around us,and the Sun itself would become part of that same dense far-off wall of stars, the Milky Way!
Most of the stars that populate space are smaller than the Sun, and certain exotic kinds are smaller than Mercury or the Moon. But others are incredibly larger.
Thus a "giant" star such as Arcturus, about 25 times wider than the Sun, would have to be represented in our model by a ball 6 yards across. Rigel, a "super- giant" 50 times wider that the Sun, would be a ball 11 yards across-the size of a whole classroom. If we stood it in place of the Sun, it would reach most of the way out to the first planet, Mercury. Red supergiants are larger still: Antares, 700 times wider that the Sun, would be about 160 yards across, so that Mercury, Venus, Earth, and Mars would be orbiting deep inside it! Betelgeuse is thought to vary from about 550 to 1000 times the width of the Sun, so that if substituted for the Sun it would be a colossal ball of 260 yards with Jupiter barely clearing its surface. (One more, the dark companion of the star Epsilon Aurigae, used to be regarded as the largest star known, 2800 times wider than the Sun-large enough to swallow the solar system to well beyond Saturn. But it is more likely some kind of cloud.)
Yet these monsters, like all stars, are so far away that they appear to us as points with no width at all.
(The Sun itself, in its "red giant" phase, will swell up like this and put an end to us-about 4,000,000,000 years from now.)
If you mention these facts during the walk, you are likely to stir up curiosity as to where these humongous stars can be seen. The Astronomical Calendar will show where, and also whether they can be seen at all at the necessary season. Epsilon Aurigae is almost circupolar, so it is visible at all seasons. It is the top of the little triangle of stars just down-right from Capella. Here again is an example of how much better it is to have done the Thousand-Yard Walk before anything else. I have often, while showing people the sky, drawn their attention to Epsilon Aurigae and told them they might be looking at the largest star; it has a certain interest, of course, but it has no such impact as when they have previously seen, the Sun Ball and the 247 paces to Saturn.
Globular clusters are awesome balls of up to a million stars, in a space perhaps 150 light-years across. In photographs such a cluster looks like a swarm of luminous bees, ever thicker toward the core, which appears a solid unresolved white. It seems as if the stars must be almost touching and the space among them must be white hot, burning with light. And in fact these stars are 25,000 times more densely packed than normal. Yet this means that they still average about a tenth of a light-year apart-in our model a mere hundred miles from each other instead of four thousand.
Even these densest aggregates of stars are mostly empty space.Since the discoveries of Rutherford and Bohr about 1911, we have thought of the atom by means of the "planetary model"; a "Sun" (the nucleus) orbited by smaller "planets" (electrons). But there are great differences.
Leaving aside the entirely distinct natures of the bodies and the orbits, there is a difference in relative sizes: the spaces within the atom are even larger a hundred times larger-than the spaces within the solar system!
The distance from the Sun out to Mercury is about 45 Sun-widths. But the distance from the nucleus out to the nearest electron-orbit it on the order of 5,000 nucleus-widths. (There are nuclei of various sizes.) So, if our model were to represent the atom instead of the solar system, the "Sun" (nucleus) would have to be a ball 100 times smaller (the size of a peppercorn) and the "planets" (electrons) far too small to be visible; either that, or we would have to spread the objects 100 times farther apart.
Truly, the universe is mostly empty space, with very rarely encountered stars and planets. Yet even the matter of which those stars and planets-and people- are made is far emptier space, with far more rarely encountered particles.